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9x(x-4)=81
We move all terms to the left:
9x(x-4)-(81)=0
We multiply parentheses
9x^2-36x-81=0
a = 9; b = -36; c = -81;
Δ = b2-4ac
Δ = -362-4·9·(-81)
Δ = 4212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4212}=\sqrt{324*13}=\sqrt{324}*\sqrt{13}=18\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-18\sqrt{13}}{2*9}=\frac{36-18\sqrt{13}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+18\sqrt{13}}{2*9}=\frac{36+18\sqrt{13}}{18} $
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